1. Field of the Invention
The present invention relates to an exposure apparatus and a method of manufacturing a device.
2. Description of the Related Art
To manufacture a semiconductor device, an exposure apparatus is used, which projects the pattern of a reticle (mask) onto a substrate by using a projection optical system and transfers the pattern. In the exposure apparatus, the substrate stage which holds a substrate can move along a plane perpendicular to the optical axis of the projection optical system to illuminate exposure light at a desired position on the substrate.
FIG. 14 is a graph showing temporal changes in the position of a substrate stage when the substrate stage is moved to a target position. Referring to FIG. 14, the abscissa takes the time [s] and the ordinate takes the error between the position of the substrate stage and a target position (to be referred to as a “stage error” hereinafter). The substrate stage generally converges to a target position while overshooting the target position. As shown in FIG. 14, the exposure apparatus performs exposure while the substrate stage converges to the target position to some extent. In an exposure period as well, however, since the vibration of the substrate stage due to the movement has not completely stopped, the substrate stage exists at a position deviated from the target position (that is, the position of the substrate stage does not completely match the target position).
A stage error in an exposure period is a factor that causes the positional shift of the pattern transferred to a substrate. More specifically, the average of stage errors in an exposure period appears as the positional shift of a pattern. It is therefore important to reduce stage errors in an exposure period. In addition, recently, in order to improve the productivity of an exposure apparatus, it is required to shorten settling time which means a period that the overshoot gradually settles down before exposure.
Under the circumstance, Japanese Patent Laid-Open No. 2004-030553 discloses a technique (model prediction control) which can predict a stage error by modeling input-output responses for a substrate stage (input: target position of a substrate stage, output: actual position of a substrate stage). If it is possible to predict a stage error, a target position may be given to the substrate stage so as to reduce the stage error.
It is, however, impossible to make a completely accurate model, and hence it is impossible to eliminate the stage error completely due to the modeling error. In an exposure apparatus, since the average of stage errors in an exposure period appears as the positional shift of a pattern, it is necessary to model the transfer characteristic of the substrate stage during the movement and the exposure. In other words, it is necessary to model a time schedule when the substrate stage starts to move and stop, and when the exposure starts and stops. But in reality, an actual exposure apparatus does not operate completely in accordance with the modeled time schedule. Thus the time lag causes a modeling error. Especially the exposure time lag deviates. Its modeling error cannot be neglected.